ITA Matrix uses cached results, which often are slightly more out-of-date, while Google Flights actually checks with the airlines and online travel agencies (OTAs) once you get to the final page with the full itinerary and the links to book.
When I try to search the same itinerary using ITA Matrix now, it only gives me a $826 price.
Similarly, BookWithMatrix for this ITA Matrix itinerary only shows $826 with Priceline/Flight Network.
Why is such a difference present and if I am to believe Google Flights' prices since it matches the airline itself, then what's the use of MATRIX at all?
In my opinion, ITA Matrix isn't really the best choice for simple round-trips. Where it really shines is when you're trying to craft more complex itineraries, and want to:
- Filter for specific fare classes (e.g., premium economy, business, refundable economy, etc.)
- Do multi-city trips where you want to have long stopovers (e.g., for the above itinerary, if you wanted to stop in Jeddah for a few days)
P.S.: linking to ITA Matrix itineraries doesn't work with links like http://matrix.itasoftware.com/#view-details:research=LHELON-LONLHE;solution=0BiiKNqOaL7LTIIKwydj0W1/BdTnlvKKfdNNSxqccWhPQG00A. Those are links local to your computer, so I recommend either copying/pasting the whole page as text or in an image for questions on Stack Exchange or elsewhere.